**ANDREA SURROCA**

*Siegel's theorem and the* abc *conjecture*

**Pages:** 323-332

**Received:** 2 March 2004
**Revised:** 1 September 2004
**Mathematics Subject Classification (2000):** 11G30 - 11J25 - 11G50

**Abstract**:
Following N. Elkies elkies we show that the abc conjecture of
Masser-Oesterlé implies an effective version of Siegel's theorem
about integral points on algebraic curves, i.e. an upper bound
for the S-integral points where the dependence on S is explicit.
The
converse statement is also announced in this note. For both
results, the main geometric tool is a theorem of G.V. Belyi.

Home Riv.Mat.Univ.Parma